$\frac{ 1 }{ x-x^{2} }+\frac{ 1 }{ x ^{2}+x-2 }=?$

My answer is $\frac{ 2(x+1) }{ x(x-1)(x+2) }$, but it's wrong......why?

Question

$\frac{ 1 }{ x-x^{2} }+\frac{ 1 }{ x ^{2}+x-2 }=?$

My answer is $\frac{ 2(x+1) }{ x(x-1)(x+2) }$, but it's wrong......why?

anonymous · Answer

$$
x-x^2 = -x(x-1)
$$The LCM normally would have the negative in it.

anonymous · Answer

$$
(x+2) + (-x) = 2
$$

aakashsudhakar · Answer

So your first step is to take the factors of each of the fractions. That gets you: $$\frac{ 1 }{ (-x)(x-1) } + \frac{ 1 }{ (x+2)(x-1) }$$So you need to multiply the first fraction by a factor of (x+2)/(x+2) and the second fraction by a factor of (-x)/(-x) to make the denominators common. That gets you: $$\frac{ x+2 }{ -x(x-1)(x+2) }+\frac{ -x }{ -x(x-1)(x+2) }$$Adding the two together get you: $$\frac{ 2 }{ -x(x-1)(x+2) }$$If you want to go a step further and clean it up, you end up with: $$-\frac{ 2 }{ x ^{3}+x ^{2}-2x }$$